Soil & Tillage Research 68 (2002) 143–152
Soil erosion prediction and sediment yield estimation:
the Taiwan experience
Chao-Yuan Lin a , Wen-Tzu Lin b , Wen-Chieh Chou c,∗
a
Department of Soil and Water Conservation, National Chung-Hsing University, Taichung 402, Taiwan, ROC
b General Education Center, Ming-Dao University, Changhua 523, Taiwan, ROC
c Department of Civil Engineering, Chung-Hua University, Hsinchu 300, Taiwan, ROC
Received 15 January 2002; received in revised form 27 September 2002; accepted 30 September 2002
Abstract
Estimating watershed erosion using geographic information systems coupled with the universal soil loss equation (USLE)
or agricultural non-point source pollution model (AGNPS) has become a recent trend. However, errors in over-estimation
often occur due to the misapplication of parameters in the equation and/or model. Because of poor slope length calculation
definitions for entire watersheds, the slope length factor is the parameter most commonly misused in watershed soil loss
estimation. This paper develops a WinGrid system that can be used to calculate the slope length factor from each cell for
reasonable watershed soil loss and sediment yield estimation.
© 2002 Elsevier Science B.V. All rights reserved.
Keywords: Upland erosion; Sediment yield; Digital elevation model; Geographic information system
1. Introduction
Universal soil loss equation (USLE) is the standard soil loss prediction model in the Soil and Water
Technical Regulations published by the Council of
Agriculture, Taiwan government. Technicians in Taiwan need a suitable computer program that can easily
determine slope length and cover-management factors. The USLE was derived with data from small
agricultural plots. Although some authors have reported on extensive use of the USLE for large basins
(Nisar Ahamed et al., 2000), the task enlarging the
USLE applications from small plots to larger ar∗ Corresponding author. Present address: No. 496, Chung-Shan
Road, Chupei City 302, Hsinchu County, Taiwan, ROC.
Tel.: +886-920-487100; fax: +886-3-5372188.
E-mail address: [email protected] (W.-C. Chou).
eas, such as watersheds and determining the correct
values for the six major equation factors is still a
challenge.
There are a number of implicit assumptions involved in runoff generation and sediment transport
embedded in the USLE. Erosion from saturated overland flow is not explicitly considered and the sediment
deposition is not represented. For these and other
reasons, applying this model to landscapes is more
difficult than applying it to simple hillslopes. The second assumption represents a major practical problem
because the model does not distinguish the hillslope
areas that experience net deposition from those that
experience net erosion.
The data required for the USLE calculations
might be available in a geographic information systems (GIS) format so that GIS-based procedures
can be employed to determine the factor values for
0167-1987/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 1 9 8 7 ( 0 2 ) 0 0 1 1 4 - 9
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C.-Y. Lin et al. / Soil & Tillage Research 68 (2002) 143–152
predicting erosion in a grid cell via the USLE
(Kinnell, 2001). Most attempts to use GIS in conjunction with the USLE to model spatial changes in
soil loss have often proceeded without addressing the
problems related to the assumptions that are incurred
in scaling up the USLE applications from plots to
large areas. The GIS/USLE application by Ventura
et al. (1988) and Hession and Shanholtz (1988), for
example, failed to mention the need to distinguish
areas experiencing net erosion and net deposition
before applying this equation. Furthermore, the definitions for slope gradient and length used by Ventura
et al. (1988) are unclear and probably different from
those specified in the original USLE. Therefore, an
automatic extraction for the slope length spatial distribution at watershed scale in conjunction with the
USLE is necessary to avoid the above-mentioned
problems.
2. Methods and materials
2.1. Predicting soil loss with the USLE for plots
Most erosion assessments performed in North
America during the past two decades have used the
USLE (Hession and Shanholtz, 1988; Ventura et al.,
1988; Wilson, 1989). This model was derived empirically from approximately 10,000 plot-years of data
(Wischmeier and Smith, 1978) and may be used to
calculate erosion at any point in a watershed that
experiences net erosion. The USLE is written as
follows:
A = RKLSCP
(1)
where A is the average annual soil loss (t/ha per
year), R the rainfall erosivity factor (MJ/ha mm h),
K the soil erodibility factor (t/MJ h mm), L the slope
length factor, S the slope steepness factor, C the
cover-management factor and P is the supporting
practice factor.
Climate erosivity is represented by R and can be
estimated from the rainfall intensity and amounts
data. The soil erodibility nomograph (Wischmeier
et al., 1971) can be used to predict the K value. The
topography and hydrology effects on soil loss are
characterized by the L and S factors. For direct USLE
applications, a combined LS factor was evaluated for
each land cell as (Wischmeier and Smith, 1978)
m
λ
LS =
(65.4 sin2 β + 4.56 sin β + 0.0654)
22.13
(2)
where m takes the values 0.5, 0.4, 0.3, and 0.2 for
tan β > 0.05, 0.03 < tan β ≤ 0.05, 0.01 < tan β ≤
0.03 and tan β ≤ 0.01, respectively (λ is the slope
length in m; β the slope angle in degrees). Land use
and management are represented by CP and can,
with some difficulty, be inferred using remote sensing
combined with ground-truthing.
2.2. Erosion estimation for watersheds
Estimation of the L factor for a watershed contains
a particular problem in applying it to real complex
landscapes as part of GIS. Slope lengths for a given
land area should not be different when grid size is
changed. Areas experiencing net soil loss should be
specified during development methods for automated
slope length delineation in a watershed.
2.3. Flow direction of a watershed
A watershed can be described with respect to the
surface runoff as being the locus of points within an
area where runoff produced inside the area perimeter
will move into a single watershed outlet. Information
about the flow direction is recorded as an attribute of
each spatial unit within the watershed to represent the
flow direction. In this study, a 3 × 3 moving window
was used over a digital elevation model (DEM) to
locate the flow direction for each cell. The steepest
descent direction from the center cell of the window
to one of its eight neighbors was chosen as the flow
path. This neighbor is called the cell downstream of
the center cell. This method is also called the D8
(deterministic-eight node) algorithm. D8 remains the
most frequently used method for determining contributing areas, although it cannot model the flow
dispersion (Gallant and Wilson, 1996). Fig. 1 provides an example of a DEM, and the flow directions
are indicated with arrows.
A variety of methods have been developed to process DEMs automatically to delineate and measure the
C.-Y. Lin et al. / Soil & Tillage Research 68 (2002) 143–152
145
Fig. 1. A DEM and the derived flow directions.
properties of drainage networks and drainage basins
(Mark, 1983; Band, 1986; Jenson and Domingue,
1998; Tarboton et al., 1991; Martz and Garbrecht,
1992). An approach that has been widely used to
compute the flow directions and delineate watersheds
was presented by Jenson and Domingue in 1988.
It used a depression-filling technique for the treatment of flat areas and depressions. However, two
problems were encountered when this method was
applied to realistic, complex landscapes. The first
is that in some cases there might be more than one
outflow point from a depression or flat area after
the area is filled. The second is that looping depressions located on a flat surface cannot be solved.
Martz and Garbrecht (1998, 1999) proposed a complicated breaching algorithm for the treatment of
closed depressions in a DEM. Based on Jenson’s
method; a modified method in this study was developed to effectively improve dead-end problems
in depressions and flat areas. Fig. 2 shows the difference between both methods in flow direction
extraction.
Fig. 2. Difference of extracting stream network from a DEM between Jenson’s and modified method.
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2.4. Channel networks in a watershed
2.5. Delineation of slope length
Channel networks are traditionally obtained by
tracing stream channels manually from maps or airborne photos. With increasing computer power and
the availability of DEMs, attempts have been made to
extract networks from DEMs via computer programs.
The “catch-number” method was used to calculate
the catchment number for each cell, i.e. the number
of cells that contribute surface flow to any particular cell. Cells with catchment numbers greater than
a given threshold are considered to be on the flow
path. All cells with catchment numbers greater than
the threshold delineate and define the network channels. The beginning point of a channel depends on
how the channels are defined. If the beginning point
of a channel is defined at the place where a defined
amount of water has accumulated on the surface and
starts to flow downhill, the upper extent of a channel
will change with the variation in precipitation. The
variable nature of the starting points can be modeled
by adjusting the threshold according to the hydrological factors, such as rainfall intensity. The distribution
and the extent of the networks in reality can be more
closely represented with channels extracted with a
proper threshold. Fig. 3 shows that the smaller the
chosen threshold, the more detailed the channels
obtained.
As indicated by Kinnell (2001), the impact of variations in runoff from upslope caused by factors other
than space is ignored if slope length is determined
from nothing more than the drainage area as in the
current practice when the USLE is applied to grid
cells. To distinguish between overland and channel
flow, thresholds are employed to determine the proper
slope lengths. Fig. 4 depicts the overland flow path
that is derived after extracting the channel flow using a specified threshold. The threshold for channel
flow extracted in a specific watershed depends on the
hydrological and geological factors of the watershed.
Lower infiltration rate and/or higher rainfall intensity
areas are more vulnerable to gully erosion. Hence,
a lower threshold sufficient to initiate the beginning
point of a channel can be expected. In other words,
areas with higher infiltration rates will express longer
slope lengths under the same rainfall intensity. Generally, overland flow paths seldom exceed 100 m due to
the interception of natural depressions, flat areas, or
ditch construction. A threshold of 100 m can be used
as a default value to initiate the beginning point of a
channel for delineating the slope length in a watershed
in most areas. If observed data exists in practice, the
threshold can be further adjusted for the model to fit
the real world. The revised universal soil loss equation
Fig. 3. Channel networks of the Dafuko watershed inferred from DEM as the threshold changed.
C.-Y. Lin et al. / Soil & Tillage Research 68 (2002) 143–152
147
Fig. 4. Spatial distribution of overland flow illustrating portions of watershed with net erosion.
(RUSLE) (Renard et al., 1996) also indicated that surface runoff will usually concentrate in less than 400 ft.
Slope length is best determined using pacing or field
measurements. In this study case, the on site investigation indicated that 100 m was the better average
value.
2.6. Predicting sediment yield
The sediment delivery ratio concept, DR, is most
commonly defined as the ratio of sediment yield
to total soil loss. Equation may be expressed in
non-dimensional terms as
Sy
DR =
(3)
T
where Sy is the sediment yield (mass/area/time) at the
watershed outlet or point of interest, and T the total
soil loss (mass/area/time) defined as the total eroded
sediment on the areas eroding above the watershed
outlet. Conceptually, Eq. (3) is a convenient way to
estimate the sediment yield at a downstream point of
interest such as a reservoir site or a detention basin.
Soil loss estimation is usually conceptualized and
computed in the context of the universal soil loss
equation. This also introduces a limitation because
USLE does not consider gully erosion, riverbed or
bank erosion, or sediment deposition. With these ex-
clusions, USLE is most properly applied on steeper
(where the slope shape is not concave and sufficiently
steep to ensure net soil detachment) field portions,
commonly with slope lengths on the order of 100
to 102 m in length. The amount of sediment delivered from upland to the stream or watershed outlet
can be determined by multiplying the soil erosion
rates against a delivery ratio. The relationship is
given by
Ls =
(As)i × DRi
(4)
where Ls is the total amount of upland sediment delivered to the perennial stream (t per year), As the
annual soil loss (t per year) for a given cell, and DRi
the upland sediment delivery ratio of the cell i. The
upland sediment delivery ratio (DR) depends upon
the land cover, slope and distance to the stream channel. As pointed out by Wolman (1977), DR provides
a cover for the actual physical storage processes as
well as for errors in estimates of the amount eroded
and for temporal discontinuities in the sediment delivery process. Data from Taiwan’s reservoirs and
watersheds indicates that the major sediments are fine
particles such as silt and clay. Taiwan’s torrents and
gullies are over constructed by conservation structures
or retaining works, which is why slope erosion is
much more important than the riverbed contribution.
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Fig. 5. The linear relationship of annual erosion depth between
measured and estimated data (data from three major reservoirs and
one watershed in Taiwan).
Because coarse particles cannot be estimated by the
USLE and a simplified calculation is needed for
Taiwan’s watersheds, this paper considers sediments
from sheet erosion transported by overland flow until it reaches the channels. The channel flows then
carry the sediments to reservoirs or watershed outlets.
Generally, DR decreases as the overland flow length
increases because it is more difficult for sediments
to reach the channels over longer traveling distances.
We verify this assumption in the example applications
and with examples from Taiwan’s major reservoirs
and watershed (Fig. 5). The DR for a given cell i
can be calculated from the receiving drainage length
(LRi ) ratio to total drainage length (Li ):
DRi =
LRi
Li
(5)
2.7. System architecture
Successful watershed modeling for non-point pollution control depends upon how large volumes of
input data are managed and manipulated. The function used to summarize and display the model results
in a variety of forms and presentation styles that require highly flexible data management. We developed
the WinGrid spatial analysis software to generate and
organize the input parameters required by the USLE
model. In the WinGrid system, the basic data storage
unit can be represented as a single layer in a map
that contains information about the location features.
The WinGrid system consists of several separate
program components (e.g. GRIDDING, SPATIAL,
WATERSHED, MODULES, UTILITY, DISPLAY,
and IMPORT/EXPORT). Each component performs
a separate task.
The USLE modeling database generated for this
study included both spatial and non-spatial information. The spatial information consisted of digital
elevation data for characterizing the slope and aspect;
imagery data for the land use/land cover classification
and soil information. The non-spatial information included field-monitoring data, which could be used in
the model calibration and other land-related information collected during farmer surveys. These data were
processed and spatially organized at a 40 m × 40 m
grid cell resolution. The parameter values required by
the model were extracted from the WinGrid database
for each cell grid.
2.8. Example application
The study area chosen for the upland soil loss and
sediment yield evaluation was the Dafuko watershed.
This 1209.6 ha watershed is located at the headwaters of Peikang Creek, one of the major rivers in
central Taiwan. The study watershed is characterized
by mudstone resulting in poor infiltration and strong
erosion potential at the bare areas. There are several
gullies that empty into the Dafuko Creek, a tributary
of Peikang Creek. The soil texture in the watershed
consists mainly of silt and/or clay, with slopes ranging from very gentle to moderately steep. Agriculture
is predominant in 24.3% of the area and a hardwood
forest covers the remaining 75.7%. Only a negligible
portion of this area is occupied by other utilization.
The major crops in this area are bamboo, areca, tea
and citrus. The climate in this watershed is humid
and sub-tropical. The drought season is from October
to April. The long-term (1986–1999) average annual
rainfall is around 1877 mm, with the highest monthly
value at 380 mm, occurring in August. Because of
the high rainfall intensity and soil erosion potential,
farmers in the watershed are required to implement
the best management practices (BMPs) to control
excessive soil loss.
C.-Y. Lin et al. / Soil & Tillage Research 68 (2002) 143–152
149
Fig. 6. Distribution of grid cells with overland flow used to determine slope length for watershed erosion estimation with USLE.
2.9. Parameters required and manipulation
R varies on a regional scale. It can be checked on the
Taiwan rainfall erosivity map given by Huang (1979).
The soil erodibility nomograph can be used to predict
the K value. The nomograph of Taiwan’s K values was
interpolated or measured from county soil surveys by
sampling more than 113 sites (Wann, 1984). Kriging
was applied to grid the R and K values for the application site. In the WinGrid system two thresholds are
needed to determine the overland flow, intermittent
flow and perennial flow for the watershed. A threshold
of 100 m was used to separate the overland flow and
channel flow. Another threshold was used to extract
the perennial flow from the channel flow for the delivery ratio calculation. The overland flow path can then
be delineated and assumed as the slope length experiencing net erosion in the watershed (Fig. 6). Land
use and land cover information was obtained from
remote sensing data. The normalized difference vegetation index (NDVI) was used to calculate the spectral
ground-based data, which shows the highest correlation with the above-ground biomass (Lin, 1997). After
a reversal linear transformation derived from training
samples, the relationship between C and NDVI can
be established as C = ((1 − NDVI)/2), where the
C value in each land cell can be specified (Fig. 7).
Fig. 8 depicts the c factor from the NDVI calculation
compared with the land cover information. It is highly
Fig. 7. C factor from NDVI calculation compared with land cover
information.
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Fig. 8. Spatial display of the cover-management factor in the watershed.
Fig. 9. Spatial display of the sediment delivery ratio generated by the system.
correlated with Taiwan’s Soil and Water Technical
Regulations. A more accurate C factor requires an
on-site investigation. Because artificial erosion control practices are nearly absent, a P factor is usually
assigned to each land cell with a value of 1.0 in the
watershed. The watershed sediment yield can be estimated using the sediment delivery spatial distribution
ratio (Fig. 9) generated from the DEM calculation.
3. Results and discussion
The simulation results for the Dafuko Creek watershed are summarized in Figs. 10 and 11. Which
indicate the soil loss and sediment yield spatial distribution. According to the Hydrological Yearbook
of Taiwan, the average annual sediment yield for
Peikang Creek is about 2.35 × 106 t measured at a
sampling station with a watershed area of 645.21 km2 .
A 2.6 mm average annual deposition depth can be
derived from the 1.4 t/m3 bulk density calculation in
the topsoil at the Peikang Creek watershed. Because
Dafuko Creek is one of the upstream tributaries of
Peikang Creek, we obtained a similar erosion depth
calculation via this module. Using the overland flow
path as the slope length, the annual erosion depth is
in the range of 2.2–2.7 mm at the bridge sites taken
at the sub-watershed outlet along the Dafuko Creek
C.-Y. Lin et al. / Soil & Tillage Research 68 (2002) 143–152
151
Fig. 10. Spatial distribution of predicted soil erosion rates for the Dafuko watershed.
Fig. 11. Predicted sediment yield after delivery ratio calculation by Eq. (4).
(Table 1). Simanton et al. (1980) applied the USLE
to four small watersheds on Walnut Gulch located in
southeastern Arizona, USA. Two of the watersheds
had no gullies or significant alluvial channels and
represented somewhat reasonable applications of the
USLE model. USLE application to two other small
watersheds with significant gullies and alluvial channels represented a gross misapplication of the USLE
model. Wilson (1989) pointed out that the USLE
should be applied only to those parts of the landscape
that experience net erosion. The software developed
Table 1
Depths of erosion for selected sub-watersheds of Dafuko Creek
watershed estimated with USLE using modified method of extracting stream networks
Watershed outlet
Erosion depth (mm per year)
Paddy no. 1
Sen-Man
Kan-Sun
Kun-Kuan
Kan-Hua
2.7
2.2
2.5
2.6
2.2
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in this study scales up USLE applications from the
slope to the watershed.
4. Conclusion
Soil erosion involves complex and heterogeneous
hydrological processes. The USLE has been the official calculation algorithm used by Taiwan’s government. This method has been widely used to calculate
erosion at any point in a landscape that experiences
net erosion. It is simple to use and conceptually easy
to understand. The DEM is a fundamental input for
spatially distributed models and can provide primary
spatial information on elevation, slope and watershed
aspect in the modeling process. The DEM can be
integrated within the watershed system to model the
effects of these parameters upon soil erosion over the
entire watershed. This study successfully introduced
a simple method for automated spatial distribution
extraction for overland flows in conjunction with the
USLE to produce a reasonable estimation for soil
erosion and sediment yield at the watershed scale.
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